2004/08/26 by Giovanni Panti, Panti, Giovanni
Computer Science · Mathematics · #06D35 #37A05 #Advanced Algebra and Logic #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #math.DS #math.LO #msc:06D35 #msc:37A05
paper · pdf · doi:10.48550/arxiv.math/0408370
12 pages, 3 figures. Revised version according to the referee's suggestions. To appear in the J. of Pure and Applied Algebra
openalex publication_date 2004/08/26 · arxiv created 2006/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0,u] of lattice-ordered abelian groups in which a strong order unit u>0 has been fixed. They form an equational class, and the free n-generated free MV-algebra is representable as an algebra of piecewise-linear continuous functions with integer coefficients over the unit n-dimensional cube. In this paper we show that the automorphism group of such a free algebra contains elements having strongly chaotic behaviour, is the sense that their duals are measure-theoretically isomorphic to a Bernoulli shift. This fact is noteworthy from the viewpoint of algebraic logic, since it gives a distinguished status to Lebesgue measure as an averaging measure on the space of valuations. As an ergodic theory fact, it provides explicit examples of volume-preserving homeomorphisms of the unit cube which are piecewise-linear with integer coefficients, preserve the denominators of rational points, and enjoy the Bernoulli property.